All CFW's enable PS2 playback but it depends on your hardware which kind: Slim and later fat models depend on the full emulation which works but you need to test case by case how well it works - the compatibility will be the same more or less as PS2 classics method or whatever, but all you need is the PS2 iso Image and you are good to go playing it.
Some titles WILL be utterly unplayable on PS3 official/Cobra's PS2 solution without any hardware backing it up, even some 2D games like Hokuto No Ken tournament fighting game's PS2 port that is Japan only, will not be playing back in any playable speeds which is sad and made me hurt inside back when I initially tested this.